Recent findings have revived interest in the link between real wage rigidity and employment fluctuations, in the context of frictional labor markets. The standard search and matching model fails to generate substantial labor market fluctuations if wages are set by Nash bargaining, while it can generate fluctuations in excess of what is observed if wages are completely rigid. This suggests that less severe rigidity may suffice. We study a weaker notion of real rigidity, which arises only in frictional labor markets, where the wage is the sum of the worker's opportunity cost (the value of unemployment) and a rent. With wage rigidity this sum is acyclical; we consider rent rigidity, where only the rent is acyclical. We offer two contributions. First, we derive upper bounds on labor market volatility that apply if the model of wage determination generates weakly procyclical worker rents, and that are attained by rent rigidity. Quantitatively, the bounds are tight: rent rigidity generates no more than a third of observed volatility, an outcome that is closer to Nash bargaining than to wage rigidity. Second, we show that the bounds apply to a sequence of famous solutions to the bargaining problem under asymmetric information: at best they generate rigid rents but not rigid wages.

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